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p = (2q −1)2 − 2 ASALI İÇİN Q( p) REEL KUADRATİK SAYI CİSMİNİN SINIF SAYISI VE x2 − py2 = mq PELL DENKLEMİNİN ÇÖZÜLEBİLİRLİĞİ

The Class Number of The Real Quadratic Field Q( p) and The Solvability of The Pell Equation x2 − py2 = mq for The Prime p = (2q −1)2 − 2

Journal Name:

  • Trakya Üniversitesi Fen Bilimleri Dergisi

Publication Year:

  • 2005

Key Words:

Keywords (Original Language):

Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
It has been obtained a theorem so that the class number to be one of the real quadratic field the type of which the wide Richauct Degert for the p and q primes satisfying p = (2q −1)2 − 2 , ( q ≡/ 3(mod4 ). Finally it has been investigated solvability of the Pell equation x2 − py2 = mq for the primes p and q.
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Abstract (Original Language): 
p ve q , p = (2q −1)2 − 2 , ( q ≡/ 3(mod4) ) sağlayan asallar olmak üzere, bu p ve q değerine karşılık gelen geniş (wide) Richaut Degert tipinden reel kuadratik sayı cisminin sınıf sayısının 1 olması için bir teorem elde edilmiş ve bunun sonucunda aynı p ve q değerleri için x2 − py2 = mq Pell Denkleminin çözülebilirliği irdelenmiştir.
FULL TEXT (PDF): 
PDF icon arastirmax-p-2q-12-2-asali-icin-q-p-reel-kuadratik-sayi-cisminin-sinif-sayisi-x2-py2-mq-pell-denkleminin-cozulebilirligi.pdf
  • 1
113-115
  • Turkish

REFERENCES

References: 

1 ANKENY N.C., CHOWLA S., HASSE H. On the class number of the maximal real subfield of a cyclotomic field. J.
Reine Angew Math. 217, 217-220, 1965.
2 AZUHATA T. On the fundamental units and the class numbers of real quadratic fields. Nagoya Math. J. Vol. 95, pp.
125-135, 1984.
3 DEVELİ M. H., ÇALLIALP F. Some criterions for the class number of a real quadratic field of R-D type to be one. İstanbul
Üniv Fen Fak Mat Derg. 49, 13-20, 1990.
4 DICKSON L.E. Introduction to Theory of Numbers (Dever Publ. Inc. New York, 1957).
5 LANG S.D. Note on the class number of the maximal real subfield of a cyclotomic field. J.Reine Angew. Math., 290,
70-72, 1997.
6 Mc COY N.H. The theory of numbers (New York, MacMillan 1965).
7 YOKOI H. The diophantine equation x2 − py2 = m 4q and the class number of real subfields of a cyclotomic fields.
Nagoya Math. J., Vol. 91, 151-161, 1983.

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